Question

the area of a circle is 9π square inches. what is the diameter? a = 9π in² give the exact answer in simplest form. inches

Explanation:

Step1: Recall area - radius formula

The area formula of a circle is $A = \pi r^{2}$, where $A$ is the area and $r$ is the radius. Given $A = 9\pi$.
So, $\pi r^{2}=9\pi$.

Step2: Solve for radius $r$

Divide both sides of the equation $\pi r^{2}=9\pi$ by $\pi$. We get $r^{2}=9$. Taking the square - root of both sides, since $r>0$ (radius is non - negative), $r = 3$ inches.

Step3: Find the diameter $d$

The diameter $d$ of a circle is related to the radius by the formula $d = 2r$. Substituting $r = 3$ into the formula, we have $d=2\times3=6$ inches.

Answer:

6 inches